We will begin with the identity of the determinant. Let \(X\)  be a matrix, then we have the following identity as an invariant polynomial of \(X\)  (an equation which is invariant under similarity transformation of \(X \rightarrow U^{-1} X U\) ) [1]}, [2]} ,
\({\mathrm {det}}( 1 + X ) = 1 + {\mathrm {Tr}}\,X + \frac{1}{2!} \Big ( {\mathrm {Tr}}\,(X^2 ) - ({\mathrm {Tr}}\,X)^2 \Big ) + \cdots + {\mathrm {det}}\,X \,.\) 
